# Homework Help: Fourier Series of modulus[t] - example of this?

1. Mar 3, 2012

### ZedCar

1. The problem statement, all variables and given/known data

Does anyone know of a website, or a book, where I can see a worked example of the Fourier Series

f(t) = [t]
-∏<t<∏
T=2∏

Finding a0 and an

Of course, it doesn't have to be t, it could be x or any other variable.

Thank you.

2. Relevant equations

3. The attempt at a solution

2. Mar 3, 2012

3. Mar 4, 2012

### OldEngr63

You have defined the function as
f(t) = [t]
-∏<t<∏
T=2∏
but that is not the example that you show worked out. The example that you show worked out is this one
f(t) = |t|
-∏<t<∏
T=2∏
This difference being that, in the latter case, the function between - π and +π is the absolute value of t; in the original problem statement, as you gave it, [t] is not really a well defined function.

The absolute value function is an even function, so when we proceed to evaluate the coefficients for the Fourier series, the first one works out as

ao = $\frac{1}{2π}$∫π f(t) dt
= $\frac{1}{π}$∫0π t dt
=$\frac{π}{2}$

The others follow in the usual fashion with the cosine multiplication.

4. Mar 5, 2012

### vela

Staff Emeritus
That should be either n or k, not both, in your equation. Let's just use n.

What does the result of the integration give you when you assume n is odd and n is even?